bisect

Program 1.1 Bisection Method
Computes approximate solution of f(x)=0
Input: inline function f; a,b such that f(a)*f(b)<0, 
     and tolerance tol
Output: Approximate solution xc

0001 %Program 1.1 Bisection Method
0002 %Computes approximate solution of f(x)=0
0003 %Input: inline function f; a,b such that f(a)*f(b)<0,
0004 %     and tolerance tol
0005 %Output: Approximate solution xc
0006 function xc = bisect(f,a,b,tol)
0007 if sign(f(a))*sign(f(b)) >= 0
0008   error('f(a)f(b)<0 not satisfied!') %ceases execution
0009 end
0010 fa=f(a);
0011 fb=f(b);
0012 k = 0;
0013 while (b-a)/2>tol
0014   c=(a+b)/2;
0015   fc=f(c);
0016   if fc == 0              %c is a solution, done
0017     break
0018   end
0019   if sign(fc)*sign(fa)<0  %a and c make the new interval
0020     b=c;fb=fc;
0021   else                    %c and b make the new interval
0022     a=c;fa=fc;
0023   end
0024 end
0025 xc=(a+b)/2;               %new midpoint is best estimate